MOSUL, Iraq June 18 (Reuters) - It's been a week since Sunni rebels took Iraq's biggest northern city from the army and - with security forces still on the defensive - the fighters in Mosul are settling down and starting to govern their new territory.

Militants from the Islamic State of Iraq and the Levant, al Qaeda's wayward Iraqi offspring who spearheaded last week's offensive across north and western Iraq, drive around Mosul in stolen police cars and station themselves at banks and government buildings.

Haitham Abdul Salam, a 50-year-old blacksmith, says he has resumed work in his shop as life readjusts itself. He says ISIL have removed the huge blast walls from the streets as well as checkpoints in an attempt to ease traffic in the city.

"ISIL treat us in a nice way. There is no harassment, even for women. Prices for foodstuffs are less," he said, although he added that government salaries are not being paid.

The hearts and minds campaign in Mosul mirrors ISIL's tactics in Syria, where it has exploited the power vacuum left by a three-year civil war in order to take ground.

In the Syrian city of Raqqa, ISIL moved in with other rebel battalions and started providing food and money to locals. It was only once ISIL had solidified its control of Raqqa did it open courts which imposed public executions and amputations.

Then it violently evicted the rebel groups that helped it take Raqqa and destroyed religious shrines.

In Mosul, unveiled women still walk through the streets and ISIL has stayed away from Christian churches, including the Tomb of Jonah.

However, militants razed the tomb of Ibn al-Athir, an Arab philosopher, according to eyewitnesses, and state television announced on Wednesday that ISIL had in fact threatened to demolish Jonah's Tomb within three days.

ISIL are being aided by secular Baathists as well as Sunni groups that disagree with their vision of an Islamic Caliphate but share a deep hatred for the Shi'ite-led government in Baghdad.

A member of the Islamic Army, a smaller insurgent group, said ISIL had agreed to run the city in consultation with all Sunni groups through a military council and that all decisions would be consultative.

The different armed factions were debating who to nominative for governor of the city, he added. The favourites are thought to include several ex-generals from Saddam Hussein's army.

U.S. SUPPORT?

A senior Iraqi security official who is involved in decision making told Reuters that there was "no clear strategy for the Iraqi government to retake Mosul".

He said less than 100 ISIL fighters took the city of two million, exploiting the collapse of the army. Thousands of Iraqi soldiers abandoned their posts when ISIL moved in to Mosul. The military is riven with corruption and troops are demoralised by poor leadership and sectarian splits

"After (ISIL) controlled the city, they started gaining the support of the city's people -- they opened the roads, they removed the blast walls, to help the people. To send them a message that they are on the side of the people, that they are different to the military," the source said on condition of anonymity.

The security source said it would be impossible to retake Mosul without U.S. support, which would leave ISIL with territory from the Mediterranean coast in western Syria to a few miles from Baghdad in eastern Iraq.

U.S. President Barack Obama is considering military support to the government of Iraq but says it is contingent on Prime Minister Nuri al-Maliki's taking steps to broaden his Shi'ite-dominated government, a move Maliki seems unlikely to take.

Obama pulled out all U.S. troops in late 2011 and rules out sending them back, although he is weighing other options such as air strikes.

Fathi Kashmoola, a 45-year-old resident of Mosul, say he was unable to flee when the militants moved in because he could not move his four disabled brothers. He says ISIL have not harassed people but says he is anxious for his future.

"We are living in a whirlpool ... it is, frankly, not the life we would wish for. Most people near me left expecting their areas to be shelled or mortared," he said.

Usama Hassan, a university lecturer, summed up the dilemma of those who remained: "We are stuck in between the government's hammer and insurgents anvil." (Additional reporting by Raheem Salman and Isra' Al-Rubei'i in Baghdad; Writing by Oliver Holmes; Editing by Giles Elgood)

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